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Cited by 609Spatial and Panel Data AnalysisAdvanced Statistical Methods and ModelsStatistical Methods and Bayesian Inference

Heteroskedasticity-robust Standard Errors for Fixed Effects Panel Data Regression

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Stock, James H., Watson, Mark W.·2008·Econometrica
DOI 10.1111/j.0012-9682.2008.00821.x
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Abstract

The conventional heteroskedasticity-robust (HR) variance matrix estimator for cross-sectional regression (with or without a degrees-of-freedom adjustment), applied to the fixed-effects estimator for panel data with serially uncorrelated errors, is inconsistent if the number of time periods T is fixed (and greater than 2) as the number of entities n increases. We provide a bias-adjusted HR estimator that is √nT-consistent under any sequences (n T ) in which n and/or T increase to ∞. This estimator can be extended to handle serial correlation of fixed order.

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Crossref · 10.1111/j.0012-9682.2008.00821.x

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  • By using cluster-robust variance estimates, inference does not suffer from the incidental-parameters problem because the variance estimator σ̂^2_w does not rely on consistent estimation of λ_i.

    “However, by using cluster-robust variance estimates, our inference does not suffer from this problem since the variance estimator ˆ σ 2 w does not rely on the consistent estimation of λ i any more, similar to the insight of Stock and Watson (2008).”

    From Revisiting Event-Study Designs: Robust and Efficient Estimation (2024) · cites this paper as Stock and Watson (2008)

  • The candidate variance estimator ∑_i (∑_{t; it∈Ω} v_it ˆε_it)2 is numerically invariant to the underlying ˆλ*_i estimates.

    “The first challenge is that the fixed effects λ i are not generally estimated consistently (e.g., in short panels). This inconsistency, however, turns out to be inconsequential because the candidate variance estimator ∑ i ( ∑ t ; it ∈ Ω v it ˆ ε it ) 2 is numerically invariant to the underlying ˆ λ ∗ i estimates.”

    From Revisiting event study designs: robust and efficient estimation (2022) · cites this paper as Stock and Watson (2008)

  • The invariance property of ˆσ2_w derives from the invariance of ˆτ*_w to adding arbitrary unit fixed effects (or more generally A'_i ˇλ_i terms) to the outcomes.

    “This invariance property of ˆ σ 2 w derives from the invariance of ˆ τ ∗ w to adding arbitrary unit fixed effects (or, more generally, A ′ i ˇ λ i terms for some i and ˇ λ i ) to the outcomes; this was earlier pointed out by Stock and Watson (2008).”

    From Revisiting event study designs: robust and efficient estimation (2022) · cites this paper as Stock and Watson (2008)

  • Event-study estimates are often estimated via OLS, and standard covariance estimators for OLS, including cluster-robust variance estimators, produce asymptotically normal estimates as the number of clusters grows large.

    “Although somewhat more restrictive, event-study estimates are often estimated via OLS, and standard covariance estimators for OLS, including cluster-robust variance estimators, produce asymptotically normal estimates as the number of clusters grows large (Hansen, 2007;Stock and Watson, 2008;Hansen and Lee, 2019).”

    From A More Credible Approach to Parallel Trends (2023) · cites this paper as Stock and Watson, 2008

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Authors
Stock, J. H., & Watson, M. W.
Affiliations
National Bureau of Economic Research (US)
ORCID
Watson, Mark W.
Venue
Econometrica
Publisher
The Econometric Society
Published
2008-01
Volume
76
Issue
1
Pages
155-174
ISSN
  • 0012-9682 (ISSN-L)
  • 1468-0262
DOI
10.1111/j.0012-9682.2008.00821.x
OpenAlex
W2156834658
Cited by
609
References
8
Citations by year
2026: 38 · 2025: 42 · 2024: 31 · 2023: 42 · 2022: 34 · 2021: 34 · 2020: 47 · 2019: 43 · 2018: 43 · 2017: 26 · 2016: 38 · 2015: 37 · 2014: 29 · 2013: 33 · 2012: 25
FWCI
49.35
Type
journal article
Language
en
Open access
Licence
Locations
  • Econometrica (publishedVersion)
  • Digital Access to Scholarship at Harvard (DASH) (Harvard University) (submittedVersion, cc-by)
Topics
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Keywords
estimator consistency, bias correction, serial correlation, cross-sectional regression

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